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The initial position, velocity, and acceleration of an object moving in simple harmonic motion are xi, vi, and ai; the angular frequency of oscillation is w.
(a) Show that the position and velocity of the object for all time can be written as
x (t) = x i cos wt + (vi/w) sin wt
v (t) = ─ xiw sin wt + vi cos wt
(b) If the amplitude of the motion is A, show that v2 ─ ax = vi2 ─ aixi = w2A2 |
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